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Adventures with Monte Carlo Simulations of the Self-Avoiding Walk

The Rosenbluth Method is a classical kinetic growth Monte
Carlo algorithm for growing a self-avoiding walk by appending steps to its
endpoint.

This algorithm

can be generalised by the implementation of more general
elementary moves (for example, BFACF elementary moves) to realise kinetic
growth algorithms for lattice polygons.
This generalises the counting principle that underlies the Rosenbluth
method and the result is a widely applicable class of algorithms which may be
used for microcanonical sampling in discrete models. In addition to self-avoiding walks, several
applications of kinetic growth and canonical Monte Carlo algorithms will be
presented, including the sampling of trivial words in abstract groups, as well
as knotted lattice polygons and discrete lattice spin systems such as the Potts
model.

This is work was done in collaboration with Andrew
Rechnitzer of the Mathematics Department at the University of British Columbia.